Math, asked by yatamanishmudhiraj, 8 months ago

find the zeros of the quadratic polynomial of x2-4 and verify the relationship between zeroes and coefficientsata​

Answers

Answered by adwaitjoshi28
18

Answer:

Step-by-step explanation:

Let p(x)=x2−4=x2−22=(x−2)(x+2)

∴ p(x)=0

⇒ (x−2)(x+2)=0

⇒ x−2=0 or x+2=0

⇒ x=2 or x=−2

∴ Zeroes of p(x)are 2 and -2.

Now,  sum of zeroes =2+(−2)=0=−01=−coefficient ofxcoefficient ofx2

and   product of zeroes =(2)(−2)=−4=−41=coefficient termcoefficient ofx2  Hence Verified.

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Answered by Agastya0606
10

Given:

A quadratic polynomial x2 - 4.

To find:

The zeroes of the given quadratic polynomial. Also, verify the relationship between zeroes and coefficients.

Solution:

As given, we have a quadratic polynomial

 {x}^{2}  - 4

This can be written as

 {(x)}^{2}  - \:  {(2)}^{2}

 = (x + 2)(x - 2)

[as \:  {x }^{2}  -  {y}^{2}  = (x - y)(x + y)]

So, the value of the polynomial will be zero, if

x =  - 2 \: and \: 2

Now,

as we know that in a polynomial ax2 + bx + c, the sum of zeroes is

 =  \frac{ - b}{a}

and

product of zeroes

 =  \frac{c}{a}

Where a, b and c are coefficients.

Now,

In the given polynomial x2 - 4, a = 1, b = 0 and c = -4.

So,

 \frac{ - b}{a}  =  \frac{0}{1}  = 0

 \frac{c}{a}  =  \frac{ - 4}{1}  =  - 4

Also,

the sum of zeroes

  - 2 + 2 = 0

Product of zeroes

 - 2 \times 2 =  - 4

As

Sum \:  of \:  zeroes =  \frac{ - b}{a}  = 0

and

Product \:  of \:  zeroes =  \frac{c}{a}  =  - 4

Hence, the zeroes of the given quadratic polynomial are -2 and 2.

Also, the relationship between zeroes and coefficients is verified.

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